Missing values are prevalent in clinical data. They provide both challenges and information for predicting clinical outcomes. Standalone imputation models [1]}, [2]}, [3]} impute missing values at the preprocessing stage. However, imputation in the preprocessing stage prevents models from exploiting predictive information associated with gaps. Recently, researchers introduced imputation approaches that can be integrated with predictive models in an end-to-end manner. RNN-based imputation models, such as GRU-D [4]} and BRITS [5]}, demonstrate better performance when learning on sequential data with missing values. However, the recurrent nature of these models makes it difficult to perform imputation and predictions on long sequences. An alternative to imputation is to treat data with missing values as irregularly sampled time series. In this direction, models like multi-task Gaussian process RNN (MGP-RNN) [6]} and neural ordinal differential equations (ODE) based RNN [7]} have been proposed to accommodate the irregularity by creating evenly-sampled latent values. However, these models are computationally prohibitive for long sequences as they either operate with a very large covariance matrix or forward intermediate values to an ODE solver numerous times. We note that the aforementioned imputation approaches are not suitable for handling large gaps in time series that are common in intraoperative data, because uncertainty in missing values grows with the time elapsed from the last observed data. Moreover, the large gaps in intraoperative time series may reflect information of the surgery. In the design of kernelized local attention, we overcome this issue by taking advantage of the characteristics of locality and using 0s to represent the missing values. This design can encode the gap information, which helps capture clinical information associated with the gaps.
